please read http://www.co.san-juan.wa.us/cdp/Stormwater/SW_Docs_Forms/Minimum_Requirements_1.pdf

I know of past rainfall sites I have visited with daily amounts record to as low as they can get or 0.01 inch is the typical smallest unit of most raingauges (based anyway on my memory).  Now I am with you, in not wanting to call every 0.01 inch a storm for analysis and keeping track of.  If you meant 0.08 to 0.12, I would go with 0.10 inch as the separation point or basically 2-3 mm if metric. But it may depend on the goals of your study and where you live.  In Lima Peru, they get 1 cm per year, so they obviously would keep track of smaller storms than say the rainforest with 2000-3000 mm per year.  As long as you define what your value is, you should be good.  If you are studying less frequent to major events, you might want to start at 1 inch and work up.  But if you did not in Lima, you might be waiting a few decades to get enough storms larger than an iinch to analyze.

Perhaps there is no standard rainfall threshold , they all vary per region for example the tropics , mid latitudes and poles have different minimums and maximums , basically thresholds are climate specific. Therefore modeling a minimum threshold for your area of interest would be vital and perhaps new literature for that region.